Tukey's HSD Post Hoc Test Example

Problem: Susan Sound predicts that students will learn most effectively with a constant background sound, as opposed to an unpredictable sound or no sound at all. She randomly divides twenty-four students into three groups of eight. All students study a passage of text for 30 minutes. Those in group 1 study with background sound at a constant volume in the background. Those in group 2 study with noise that changes volume periodically. Those in group 3 study with no sound at all. After studying, all students take a 10 point multiple choice test over the material. She begins by conducting a One-way, between-subjects Analysis of Variance. She finds a significant F score. The relevant variables from her ANOVA table are:

MS_within =4.18; M₁ =6; M₂ =4; M₃ =3; df_within = 21; n = 8

*(according to the Tukey's sig/probability table, taking into account (df_within = 21 and treatments = 3), the mean comparison between means 1 and 3 is statatistically signficant, but not the other comparisons).

Interpretation: Susan's hypothesis was only partially supported in that those who studied with a constant noise did perform signficantly better on the test than those who studied without any noise, but they did not perform signficantly better than those who studied with random noise.